Numerical investigation of non-Newtonian fluids in annular ducts with finite aspect ratio using lattice Boltzmann method

Abstract

In this work the instability of the Taylor-Couette flow for Newtonian and non-Newtonian fluids (dilatant and pseudoplastic fluids) is investigated for cases of finite aspect ratios. The study is conducted numerically using the lattice Boltzmann method (LBM). In many industrial applications, the apparatuses and installations drift away from the idealized case of an annulus of infinite length, and thus the end caps effect can no longer be ignored. The inner cylinder is rotating while the outer one and the end walls are maintained at rest. The lattice two-dimensional nine-velocity (D2Q9) Boltzmann model developed from the Bhatnagar-Gross-Krook approximation is used to obtain the flow field for fluids obeying the power-law model. The combined effects of the Reynolds number, the radius ratio, and the power-law index n on the flow characteristics are analyzed for an annular space of finite aspect ratio. Two flow modes are obtained: a primary Couette flow (CF) mode and a secondary Taylor vortex flow (TVF) mode. The flow structures so obtained are different from one mode to another. The critical Reynolds number Re(c) for the passage from the primary to the secondary mode exhibits the lowest value for the pseudoplastic fluids and the highest value for the dilatant fluids. The findings are useful for studies of the swirling flow of non-Newtonians fluids in axisymmetric geometries using LBM. The flow changes from the CF to TVF and its structure switches from the two-cells to four-cells regime for both Newtonian and dilatant fluids. Contrariwise for pseudoplastic fluids, the flow exhibits 2-4-2 structure passing from two-cells to four cells and switches again to the two-cells configuration. Furthermore, the critical Reynolds number presents a monotonic increase with the power-law index n of the non-Newtonian fluid, and as the radius ratio grows, the transition flow regimes tend to appear for higher critical Reynolds numbers.

Enhanced Lattice Boltzmann modelling of axisymmetric flows

“…Comparisons of the maximum stream function values in the r-z plane for cases with Re ¼ 85, 100 and 150 that are listed in Table 1, showing that the present model compares well with average values from the literature. The average errors of the present method are smaller than those of Khali et al (2013) for Re ¼ 85 and 150 and similar for Re ¼ 100.…”

“…For comparisons with the results available in the literature, the Reynolds number is used in the study and several Reynolds numbers were selected for different cases. After steady solutions were obtained, the numerical results were compared with those of Liu (1998), who proposed a differential quadrature method to solve the vorticity-stream function formulation in the cylindrical polar system, and Khali et al (2013) who used the method of Huang et al (2007) to simulate similar cases.…”

“…As most applications of flows involve non-Newtonian fluids, the model has been extended to simulate non-Newtonian TaylorCouette flows. The same problem as used by Khali et al (2013) is applied to the validation and is shown in Figure 2. The ratio of inner cylinder radius to outer cylinder radius was chosen to be ç ¼ 0 .…”

“…In the present test, the rotation speed is low and the relationship of the shear rate is defined by (Khali et al, 2013) ª…”

Non-Newtonian flow effects on the coalescence and mixing of initially stationary droplets of shear-thinning fluids

“…This was achieved by replacing the constant relaxation time in the classical Bhatnagar-GrossKrook (BGK) model by one that is shear-rate dependent [31][32][33][34]. For the present simulation based on the MRT model, the relaxation parameter s ν in the collision matrix = diag(s ρ ,s e ,s ε ,s j ,s q ,s j ,s q ,s ν ,s ν ) is modified to depend on the local shear rate.…”